Data Reduction and Analysis Techniques. Continuum - Point Sources On-Off Observing

Transcription

1 Data Reduction and nalysis echniques Ronald J. Maddalena Continuum - oint ources On-Off Observing Noise Diode ignal ignal Observe blank sky for 10 sec Move telescope to object & observe for 10 sec Move to blank sky & observe for 10 sec Fire noise diode & observe for 10 sec Observe blank sky for 10 sec Detector 1

2 Continuum - oint ources On-Off Observing Continuum - oint ources On-Off Observing Known: Equivalent temperature of noise diode or calibrator ( cal ) 3 K Bandwidth ( ν) 10 MHz Gain K / Jy Desired: ntenna temperature of the source ( ) Flux density () of the source. ystem emperature( s ) when OFF the source ccuracy of antenna temperature ( )

3 Continuum - oint ources On-Off Observing cal cal _ off cal cal cal _ off ( ) 0 K 6 K 6 K ν t s 0.00 K NR 3000 Continuum - oint ources On-Off Observing noise estimate 1. Write down data analysis equation: cal cal _ off. Use propagation of errors : i i 3. Use the following substitutions : ( ) ν t ν t G k 1 ν t 3

4 Continuum - oint ources On-Off Observing noise estimate cal cal _ off ( ) i i + refrence + cal_ on Cal refrence cal_ on + cal _ on cal _ on cal_ off 1 NR ( + ) + ( ) ( cal _ on ) + ( cal _ off ) ( ) ( cal _ offl ) + ( cal _ off ) ( ) 1 + ν t NR ( 10 ) ~ 900 ( Not 3000! ) refrence Continuum - oint ources ssumptions: Classical Radiometer equation assumes: Narrow bandwidths, Linear power detector, << s, Noise diode temperature << s, t t t cal_on t cal_off Blanking time << t No data reduction! 4

5 hases of an Observation otal ower Noise Diode witching ignals Detector Cal On Detector Cal Off hases of an Observation otal ower cal 4 K s 100 K theor 0.1 K meas 1 K hapes very similar Excess noise from atmospheric fluctuation 5

6 hases of a Observation Beam witched ower ignal Reference Noise Diode witching ignals Detector ig Cal On Detector ig Cal Off Detector Ref Cal On Detector Ref Cal Off hases of a Observation Beam witched ower Noise Diode witching ignals Detector ig Cal On Detector ig Cal Off Detector Ref Cal On Detector Ref Cal Off 6

7 hases of a Observation Double Beam witched ower ignal Reference Noise Diode witching ignals Detector ig Cal On Detector ig Cal Off Detector Ref Cal On Detector Ref Cal Off Continuum - oint ources Beam-witched Observation cal ( + ) cal ( + ) 7

8 Continuum - oint ources On-he-Fly Observation Beamwidth osition s Continuum - oint ources On-he-Fly Observation If total power: cal ( + ) If beam-switching (switched power): ( cal _ on + _ ) cal cal off cal _ off ( cal _ on + _ ) cal cal off 8

9 Baseline Fitting olynomials et order of polynomial Define areas devoid of emission Creates false features Introduces a random error to an observation + eak olynomial Why olynomials? Continuum - oint ources Gaussian Fitting Define initial guesses et flags to fit or hold constant each parameter et number of iterations et convergence criteria Fitted parameters Chi-square of the fit arameter standard deviations Restrict data to between the half power points for fitting to a telescope s beam Multi-component fits should be done simultaneously 9

10 Continuum - oint ources Gaussian Fitting Where is noise the highest? Where is noise the lowest? changes across the observation. Weights (1/ ) for least-square-fit changes across the observation. For strong sources, should worry about using proper weights in data analysis. emplate Fitting Create a template: ufficient knowledge of the telescope beam, or verage of a large number of observations Convolve the template with the data > x-offset. hift by the x-offset. erform a linear least-squares fit of the template to the data: lways try to fit physicallymeaningful functions 10

11 veraging Data / tmosphere s changes due to atmosphere emission. Use weighted average with weights 1/ 1 1 j j avrg j 1 1 j changes due to atmosphere opacity. Opacity from the literature or theory, from a tipping radiometer, from atmospheric vertical water vapor profiles, or by tipping the antenna ' ' e tau /sin( el) e tau /sin( el) Gain Correction * * ' ' / η / η or * B * B ' ' / η M / η M 11

12 Continuum - Extended ources On-he-Fly Mapping elescope slews from row to row. Row spacing: ~0.9 λ /D few samples /sec. Highly oversampled in direction of slew <0.3 λ /D Could be beam switching Convert ower into. Fit baseline to each row? Grid into a matrix Continuum - Extended ources On-he-Fly Mapping - Common roblems triping (Emerson 1995; Klein and Mack 1995). If beam-switched, Emerson, Klein, and Haslam (1979) to reconstruct the image. Make multiple maps with the slew in different direction. 1

13 GB Continuum Images Rosette GB Continuum Images M17 13

14 GB Continuum Images W3 GB Continuum Images - Orion 14

15 pectral-line - oint ources On-Off Observing Noise Diode ignal ignal Observe blank sky for t sec Fire noise diode to determine s Move telescope to object & observe for t sec Can observe an extended source using this technique -- observations arranged in a grid map. Detector pectral-line - oint ources osition-witched Observing 15

16 pectral-line - oint ources osition-witched Observing ( f ) s ( f ) moothed/veraged s of Denominator s ( f ) cal K ~ ν / N ignal (line expected) channels t 1 ( f ) + ( f ) + t Reference (No line expected) 1 + ( f ) ( f ) s M _ Channels But only for weak lines and no strong continuum! Constant depends upon details of the detecting backend hases of a Observation witched ower Frequency witching ignal Frequency Reference Frequency Local Osciflator Noise Diode witching ignals Detector ig Cal On Detector ig Cal Off Detector Ref Cal On Detector Ref Cal Off 16

17 pectral-line - oint ources Frequency-witched Observing - In band ignal s (REF)*[(IG-REF)/REF] Reference Line appears twice should be able to fold the spectra to increase NR pectral-line - oint ources Frequency-witched Folding In Band ( f ) ( f ) ( f ) ( f ) ( f ) ( f ) + ( f + f ) ( f + f ) ( f + f ) ( f) ant ( f ) ( f) ( f ) ( f) ( f + f ) ( f + f ) ( f + f ) 17

18 pectral-line Baseline Fitting olynomial: same as before inusoid D REIDUL pectral-line Other lgorithms Velocity Calibration Velocity/Frequency hifting & Regriding Doppler tracking limitations moothing Hanning, Boxcar, Gaussian Decimating vs. non-decimating routines For Optimal Filtering, match smoothing to expected line width Filtering low pass, high pass, median, Moments for Integrated Intensities; Velocity centroids,. 18

19 pectral-line RFI Excision pectral-line Mapping Grid or On-the-Fly DEC Velocity R 19

20 pectral-line Mapping Grid and On-the-Fly W V max ( α, δ ) ( α, δ, V i ) Vi Vi Vmin (If V1V > Channel Map) Velocity DEC δ For {vvmin} {v <vmax} {v++} { if (α,,v) > min then W(α, )W(α, )+ (α,,v) endif endfor R pectral-line Mapping Grid and On-the-Fly Velocity (osition-velocity map) DEC δ ( α, V ) max ( α, δ, V ) δ δ min R 0

21 pectral-line Mapping he Future of ingle-dish Data nalysis Increase in the use of RDBM. upport the analysis of archived data. ophisticated visualization tools. ophisticated, robust algorithms (mapping). Data pipelining for the general user. utomatic data calibration using models of the telescope. lgorithms that deal with data sets. nalysis systems supported by cross-observatory groups More will be done with commercial software packages 1